一个几何不等式的注记

设A是n维欧氏空间E~n中的一个非退化单形,它的切点单形为B,又以A的顶点和它的内切球心的连线与A的n+1个侧面的交点为顶点的单形设为D。若单形A,B,D的体积分别记为V(A),V(B),V(D),本文证明了V(B)≤V(D)≤(1/n~n)V(A)。     

微积分中引入辅助函数证明不等式方法探讨

对微积分中引入辅助函数证明不等式进行了分类、总结,并通过多个实例进行了分析、证明。     

关于T凸函数的不等式

In this paper, the Tφ-convex functions were introduced as a generalizations of convex functions. Then the characteristics of the Tφ-convex functions were discussed. Furthermore, some new inequalities for the Tφ-convex functions were derived.     

动态规划在货物归并问题中的应用及优化

以动态规划方法解决货物归并问题为例,阐述如何进行动态规划算法的分析设计,并在此基础上利用四边形不等式,减少动态规划过程中每一阶段的状态转移数,从而整体上降低动态规划的时间复杂度,使其能够适用于更大规模计算．这种优化方法具有通用性,对于状态转移方程与之类似且能满足四边形不等式的动态规划问题,都可以采用相同的优化方法进行优化．     

关于Gamma函数的几个不等式

利用Gamma函数的性质,推广了一个常用不等式,得到了几个比较有价值的结果.     

A new neural network model for the feedback stabilization of nonlinear systems

A new neural network model termed ＇standard neural network model＇ （SNNM） is presented, and a state-feedback control law is then designed for the SNNM to stabilize the closed-loop system. The control design constraints are shown to be a set of linear matrix inequalities （LMIs）, which can be easily solved by the MATLAB LMI Control Toolbox to determine the control law. Most recurrent neural networks （including the chaotic neural network） and nonlinear systems modeled by neural networks or Takagi and Sugeno （T-S） fuzzy models can be transformed into the SNNMs to be stabilization controllers synthesized in the framework of a unified SNNM. Finally, three numerical examples are provided to illustrate the design developed in this paper.     

论按资源分配

合理的收入分配制度是社会公平的重要体现,市场经济的实质是寻找资源的最优化配置并产生最大的效益。基于效率公平观,配置产生的效益应按资源在配置中的贡献来分配,并通过市场对该种资源的需求程度来实现资源的价值量化。资源按其所属范围可分为私有资源和共享资源,私有资源的差异性、多样性决定了分配的差异性、多样性。法律和市场经济规则应保障个体对共享资源占有或支配的机会均等。从按资源分配的角度,对我国目前社会分配不公平等现象产生的原因及解决办法进行了初步分析。     

The children of the educational expansion era in Germany: education and further training participation in the life‐course

In this article, we examine the social dimension of inequality in educational participation. We look at the social transmission and gender‐specific channelling of education and further training in the context of employment and family. Based on quantitative survey data and qualitative interview data collected from a multi‐level empirical life‐course study (Hamburg Biographical and Life‐Course Panel: 1980–2006) conducted with a sample of the 1979 cohort of secondary school graduates in Hamburg, Germany, we discuss the education and further training practices in their lives – with special emphasis on social class of origin and gender.     

The logarithmic mean

The inequality between the arithmetic mean (AM) and geometric mean (GM) of two positive numbers is well known. This article introduces the logarithmic mean, shows how it leads to refinements of the AM-GM inequality. Some applications and properties of this mean are shown. Some other means and related inequalities are discussed. Rajendra Bhatia is a Professor at the Indian Statistical Institute, New Delhi. Some of his recent work is on means of matrices. But he is not a mean theorist.     

Euler不等式的再推广

应用几何不等式理论与解析方法,研究了n雏欧氏空间En中n维单形外接球半径与内切球半径之间的关系,建立了涉及单形外接球半径与内切球半径的一些几何不等式,进一步改进了著名的Euler不等式.